This document discusses cerebral blood flow and brain metabolism. It begins with an outline of the topics to be covered, which include cerebral blood flow, vascular anatomy, the blood brain barrier, cerebrospinal fluid, factors regulating blood flow, problems with blood flow and metabolism, and brain metabolism problems. It then goes on to describe the vascular anatomy that supplies blood to the brain, including the internal and external carotid arteries and vertebral arteries. It also discusses the circle of Willis, microcirculation in the brain, the blood brain barrier, cerebrospinal fluid, and factors involved in regulating cerebral blood flow such as blood pressure, vascular resistance, autoregulation, and metabolic mediators.

1. “Cerebral Blood Flow & Brain Metabolism”
College of Health Sciences
School of Medicine
Department of Medical Physiology
P.by: Habtemariam Mulugeta
ID No. GSR/2895/14
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2. “Cerebral Blood Flow – (CBF) & Brain Metabolism”
Advanced Neuroscience
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Outline
 Objectives
 Introduction
 CBF & Vascular Anatomy
 Blood Brain Barrier
 Cerebrospinal Fluid
 Factors regulating CBF
 CBF Problems
 Brain Metabolism
 Brain Metabolism Problems
 Summary
 Acknowledgement
 References
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Objectives
 After completing this session, students should be able to:
Describe briefly about Cerebral Blood Flow.
Explain about Regulation of Cerebral Blood Flow.
Differentiate the Factors affecting Cerebral Blood Flow.
Appreciate the Problems of Cerebral Blood Flow.
Familiarize with the Brain Metabolism.
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5. 5
Introduction
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 Skull is a closed structure.
 Most of it's content is brain tissue while some of it is
blood and CSF.
 Brain occupies 2% of the total body weight.
 Cerebral Vasculature has unique Anatomy &
Physiology.
 Brain is highly vulnerable to disruption in blood flow.
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Monro-Kellie doctrine
Figure 1 – The intracranial components and
their respective volumes

6. 6
Cont.
 Blood Supply
 750 ml/min
 55 ml/100 gm/min
 14% of total Cardiac output
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 Oxygen Supply
 46 ml/min
 3.3 ml/100 gm/min
 18.4% of total O2 consumption
 CBF: is the blood movement to the brain.
 Supplies Oxygen, glucose and nutrients.
 Remove CO2, Lactic acid & metabolites.

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CBF & Vascular Anatomy
 The left and right common carotid arteries supply most of the blood to the
head and neck.
 They travel parallel immediately lateral to either side of the trachea.
 At the superior border of the thyroid cartilage, each artery divides into:
 External Carotid Artery that supplies structures external to the skull
 Internal Carotid Artery that supplies internal skull structures.
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Cont.
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Figure 2 – Branches of External
carotid arteries

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Internal Carotid Artery (ICA)
 arise from common carotid arteries (neck)
 branches only after it enters the skull through the carotid canal
 Once inside the skull, it forms multiple branches, including:
 Anterior and Middle cerebral arteries, which supply the brain
 Ophthalmic arteries, which supply the eyes.
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Cont.
 Internal carotid arteries and their branches: are considered as anterior
circulation of brain.
 Anterior cerebral arteries: are connected by anterior communicating artery.
 ICA near its termination: is connected to posterior cerebral artery (PCA) by
Posterior communicating artery.
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Vertebral Arteries:
 Emerge from the first part of subclavian artery.
1. Pre-vertebral parts: begin in the root of the neck
2. Cervical parts: in transverse foramina of C1-C6 vertebrae.
3. Atlantic parts: perforate dura, arachnoid & enter through foramen
magnum.
4. Intracranial parts: at pons form basilar artery.
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12. 12
Cont.
 Basilar artery: at the clivus in pontocerebellar cistern ventral to pons & ends
by branching in to two posterior cerebral arteries.
 Vertebrobasilar arterial system & branches: are considered as posterior
circulation of the brain.
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13. 13
Cont.
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Figure 3 - Subclavian and carotid
arteries and their branches

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 Anterior Cerebral Artery: most of medial, superior surface & frontal pole.
 Middle Cerebral Artery : most of lateral surface & temporal pole.
 Posterior Cerebral Artery: most of inferior surface & occipital Pole.
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Cerebral Arteries:

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Cont.
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Figure 4 -
Schematic overview
& Distribution of
cerebral arteries

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Cerebral Arterial Circle
 Circle of Willis.
 is important anastomosis of arteries around
the sella turcica.
 roughly pentagon-shaped & on ventral
surface of brain.
 Its various components give numerous small
branches to supply the brain.
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Figure 5 – Inferior View of Circle of
Willis

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 It is formed by:
 posterior cerebral arteries
 posterior communicating arteries
 Internal carotid arteries
 anterior cerebral arteries
 anterior communicating arteries
 Function:
 equalizes blood pressure in the brain
 can provide collateral channels should
one vessel become blocked
 Normally no crossing over of blood from
one side to the other
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Cont.
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Figure 6 - Arterial circle on the
inferior surface of the brain

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Collateral Circulation
 In a normal individuals there is no net flow of blood across these
communicating arteries.
 But to maintain patency and prevent thrombosis there is to-and-fro
flow of blood.
 Their importance appears when a pressure gradient develops.
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Cont.
 Second collateral flow appears in surface connections that bridge pial
arteries
 They bridge major arterial territories:
 ACA – PCA, ACA- MCA, MCA – PCA
 They are called leptomeningial pathways or equal pressure pathways.
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Cerebral Microcirculation
 Capillary density in grey matter is 4 times higher than white matter.
 Pre-capillary vessels divide and reunite to form anastomotic circle called as Circle of
Duret.
 They are highly tortuous and irregular.
 Velocity of RBC’s is higher in these capillaries.
 To facilitate transfer of substrate and nutrients RBC’s have to traverse longer distance
via these capillaries
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22. 22
Cont.
 The brain capillaries are much less “leaky” than are capillaries in other
portions of the body.
 Capillaries in the brain are surrounded by “glial feet,” which provide
physical support to prevent overstretching of the capillaries in the event
of exposure to high pressure.
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Cont.
 Cerebral capillaries:
 are non-fenestrated & with tight junctions
between endothelial cells, except the capillaries
in choroid plexus which are fenestrated.
 Few vesicles in endothelial cells
 Limited diffusion & vesicular transport
 Surrounded by end feet of astrocytes; induce
tight junctions in endothelial cells
 Anatomic basis for BBB.
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Figure 7 - Cerebral capillary

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Blood Brain Barrier (BBB)
 Continuous non-fenestrated capillaries make up BBB.
 Tight junctions between capillary endothelial cells.
 Paucity of the vesicles in the endothelial cytoplasm.
 Presence of numerous carrier-mediated & active transport mechanisms in cerebral
capillaries.
 The blood-CSF barrier is due to tight junctions in choroid plexus endothelial cells.
 The capillaries in choroid plexus are fenestrated with no tight junctions.
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Cont.
 Properties of BBB
 Only few substances can freely diffuse through BBB.
 CO2, O2, water & free forms of steroid hormones.
 H+ & HCO- only slowly penetrate the BBB.
 Proteins, polypeptides & protein bound forms of hormones do not cross BBB.
 Glucose is transported by GLUT1 transporter.
 Active transporters are also present
 various ions (Na+ - K+ -2Cl- co transporter )
 thyroid hormones, organic acids, choline, nucleic acid precursors, amino acids etc.
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Significance of BBB
 It maintains the homeostasis in CNS.
 Protects the brain from endogenous & exogenous toxins.
 Prevents the escape of neurotransmitters into general circulation.
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Circumventricular Organs
 The parts of the brain which have fenestrated capillaries and thus no BBB.
 The circumventricular organs provide a window for the interaction of brain with blood.
 Posterior pituitary with Median Eminence
 Area Postrema
 Organum Vasculosum of Lamina Terminalis (OVLT)
 Subfornical Organ (SFO)
 Anterior pituitary & Pineal Gland
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Cerebrospinal Fluid (CSF)
 clear, colorless body fluid found within the tissue that surrounds the brain and spinal cord of
all vertebrates.
 Produced by specialized ependymal cells in the choroid plexus of the ventricles of the brain
 Absorbed in the arachnoid granulations.
 There is about 125 mL of CSF at any one time, and about 500 mL is generated every day.
 occupies the subarachnoid space and the ventricular system around and inside the brain and
spinal cord.
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29. 29
Cont.
 There is also a connection from the subarachnoid space
to the bony labyrinth of the inner ear via
the perilymphatic duct where the perilymph is
continuous with the CSF.
 The ependymal cells of the choroid plexus have
multiple motile cilia on their apical surfaces that beat to
move the CSF through the ventricles.
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Figure 8 - MRI showing pulsation of CSF

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Cont.
 A sample of CSF can be taken from
around the spinal cord via lumbar
puncture.
 CSF circulates within the ventricular
system of the brain.
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Figure 9 - Distribution of CSF

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Cont.
 CSF is derived from blood plasma and is largely similar to it except
that CSF is nearly protein-free compared with plasma and has some
different electrolyte levels.
 Due to the way it is produced, CSF has a higher chloride level than
plasma, and an equivalent sodium level.
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Significance of CSF
1. Buoyancy: The actual mass of the human brain is about 1400–1500 grams; however, the net
weight of the brain suspended in CSF is equivalent to a mass of 25-50 grams.
2. Protection: CSF protects the brain tissue from injury when jolted or hit, by providing a fluid
buffer that acts as a shock absorber from some forms of mechanical injury.
3. Prevention of brain ischemia: The prevention of brain ischemia is aided by decreasing the
amount of CSF in the limited space inside the skull. This decreases total intracranial pressure
and facilitates blood perfusion.
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33. 33
Cont.
4. Homeostasis: allows for regulation of the distribution of substances between
cells of the brain, and neuroendocrine factors, to which slight changes can cause
problems or damage to the nervous system.
5. Clearing waste: allows for the removal of waste products from the brain, and is
critical in the brain's lymphatic system, called the glymphatic system.
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Venous Drainage of the Brain
 thin-walled & valveless.
 Pierce arachnoid & meningeal
layer of dura (subdural space)
 end in the nearest dural venous
sinuses  ultimately  IJVs.
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Figure 10 – MRI Venography of Brain

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Cont.
Superior Cerebral Veins:
 are on superolateral surface of the brain
 drain into the superior sagittal sinus.
Inferior & Superficial Middle Cerebral Veins:
 from inferior, postero-inferior & deep aspects of cerebrum
 drain into cavernous, straight, transverse & superior petrosal sinus.
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36. 36
Cont.
The Great Cerebral Vein:
 is a single, midline vein formed inside the brain by the union of two
internal cerebral veins;
 merges with inferior sagittal sinus to form straight sinus.
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Cont.
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Figure 11 - Venous Drainage of the Brain
Internal Jugular Veins
Cerebral Venous sinuses
Cerebral Veins
Venous Drainage:

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Cerebral Blood Supply
 Brain accounts for 2% of body weight yet requires 20% of resting oxygen
consumption.
 O2 requirement of brain is 3 – 3.5 ml/100gm/min & in children it goes
higher up to 5 ml/100gm/min.
 That’s why brain requires higher blood supply 55ml/100gm/min is the rate
of blood supply.
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39. 39
Cont.
 Brain is having the highest energy requirement by mass.
 Even though brain constitutes less than 2% of body weight, the adult brain receives
15% of resting cardiac output and uses 20% of the total energy produced by the body.
 In children, up to 50% of the energy consumption of the body is being accounted for
by the brain.
 Much of this energy allocation is devoted to activities connected to neural signaling
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Cont.
 Cerebral blood flow = 55 to 60 ml/100 g brain tissue/min
 Cerebral blood flow (gray matter) = 75 ml/100 g brain tissue/min
 Cerebral blood flow (white matter) = 45 ml/100 g brain tissue/min
 Oxygen consumption whole brain = 46 ml/min
 Oxygen consumption whole brain = 3.3 ml/100 g/min
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Factors Regulating CBF
 Cerebral Perfusion Pressure (CPP)
 Cerebral Vascular Resistance (CVR)
 Hemodynamic Autoregulation
 Metabolic mediators and chemo-regulation
 pCO2
 pO2
 H+ concentration
 Neural control: sympathetic discharging
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Cerebral Perfusion Pressure
 It is the net pressure gradient causing blood flow to the brain.
CPP = MAP – CVP
CVP = ICP
CPP = MAP – ICP
 CPP is directly related to CBF: {Increase CPP causes increase CBF}
 Any factor affecting MAP or ICP will affect the CBF.
 CBF is maintained normal over a wide range of MAP by ‘Autoregulation.’
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Role of ICP in maintaining CBF
 The volume of blood, spinal fluid, and brain in the cranium at any time must
be relatively constant (Monro–Kellie doctrine).
 Increase ICP  Decrease CBF
 Decrease ICP  Increase CBF
 Cushing’s reflex
 ICP  Decrease CBF  VMC ischemia  Increase sympathetic discharge 
Increase BP  Increase CBF
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Cerebral Blood Flow Hemodynamics
 Q = ΔP/R
 R = 8.η.L/ π.r4
 CBF = CPP/CVR
 CPP = MAP − ICP
 MAP = [1/3× (SBP −DBP)] + DBP
 Laminar flow is described by  Hagen - Poiseuille law: Q = (π.r4. ΔP)/(8.η.L)
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45. 45
Cont.
 Contrary to the key assumptions behind the Hagen-Poiseuille law, it is not strictly
followed:
 normal blood flow is not continuous but pulsatile,
 blood vessels are not rigid and branchless tubes,
 if the rate of flow is continuously increased, there comes a point when resistance to
flow increases sharply and the flow ceases to be laminar, instead forming a turbulent
pattern,
 cerebrovascular autoregulation
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Cerebral Vascular Resistance (CVR)
 CVR = (8.η.L)/(π.r4)
 Resistance of the cerebral circulation is subject to dynamic changes in the
contractile state of vascular smooth muscle (VSM).
 Most resistance at the level of the penetrating precapillary arterioles.
 However, up to 50% of total CVR arises from smaller pial arteries (150 to 200
μm in diameter) and arteries of the circle of Willis.
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Autoregulation
 Maintains constant blood flow to the brain despite wide fluctuations in CPP.
 It is the inherent property of resistance vessels.
 Increase BP  vasoconstriction
 Decrease BP  vasodilation
 Maintains blood flow in the range of 50 – 150 mm Hg CPP.
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Cont.
 Proposed mechanisms include:
 Myogenic Mechanism: Intrinsic changes in vascular smooth muscles (VSM) tone.
 Endothelial Mechanism: the release of a variety of vasoactive substances from the
endothelium.
 Neurogenic Mechanism: periadventitial nerves in response to changes in transmural
pressure.
 Metabolic Mechanism: metabolic activity of astrocytes and neurons for regulating CBF.
 Pure changes in perfusion pressure involve myogenic response in VSM (Bayliss effect).
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Cont.
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Figure 12 – classical cerebral
autoregulation curve

50. 50
Cont.
 Venous physiology:
 Venous system contains most of the cerebral blood volume.
 Slight change in vessel diameter has profound effect on intracranial blood
volume.
 Less smooth muscle content
 Less innervation than arterial system
 But evidence of their role is less.
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51. 51
Cont.
 Pulsatile perfusion: myogenic response bring a change in perfusion pressure.
 Cardiac output (CO): may be responsible for improved CBF.
 Rheological factors:
 Related with blood viscosity.
 Hematocrit has main influence on blood viscosity.
 Flow is inversely related with hematocrit.
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Metabolic & Chemical Regulation
 Cerebral metabolic demand is the main regulator of cerebral blood flow,
 It occurs automatically, probably in response to the abundance or deficit of various local
factors - mainly metabolic byproducts and metabolic substrates:
 Carbon dioxide concentration in the brain parenchyma
 Low oxygen
 pH of the blood
 When cerebral metabolic demand is high – CBF will be higher at any given Perfusion
Pressure because CVR will decrease.
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53. 53
Cont.
 CO2: (Hypercapnia) - promotes increased CBF at any given perfusion pressure.
 PaCO2 exerts profound effects on CBF, range of 30 to 50 mm Hg.
 At normal conditions CBF has linear relationship with CO2.
 For every 1 mm Hg change of PaCO2 CBF changes by 2–4%.
 When alterations in PaCO2 have been sustained for 3 to 5 hours, there is an adaptive
return of CBF toward baseline levels.
 Hypercapnia combined with hypoxia has a magnified effect on CBF.
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54. 54
Cont.
1. Change of periarteriolar pH leads to a change in NO synthase activity;
2. NO synthase catalyzes intracellular cGMP production;
3. cGMP acts as a second messenger to affect a change in intracellular ionized Ca+2 availability
4. The upshot of all this is a decreased CVR
5. If the resistance is decreased but the pressure difference remains the same, the flow
increases.
6. The increase in flow is by about 1-2ml/100g/min for every 1mmHg increase in CO2.
Conversely, blood flow decreases as CO2 decreases.
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Cont.
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Figure 13 - cerebral blood flow with a
stable perfusion pressure as
CO2 increases

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Cont.
 Hydrogen ions: induce cerebral vasodilation in proportion to their concentration in the
cerebral blood.
 Any substance that increases the acidity of the brain, and therefore the H+ concentration,
increases CBF; such substances include lactic acid, pyruvic acid, and other acidic compounds
that are formed during the course of metabolism.
 CO2 combines with water to form carbonic acid, which partially dissociates to form H+
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57. 57
Cont.
 Oxygen:
 Elevated inspired O2 concentrations elicit CVR and decrease CBF.
 Within physiological range PaO2 has no effect on CBF.
 Hypoxia is a potent stimulus for arteriolar dilatation.
 At PaO2 50 mmHg, CBF starts to increase and at PaO2 30 mm Hg, it doubles.
 Hypoxia elicits VSM relaxation by inhibiting sarcoplasmic Ca2+ uptake and stimulating
the production of EDRF.
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58. 58
Cont.
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Figure 14 - cerebral blood flow with
relatively stable linear relationship at
normoxic or hyperoxic levels

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Neural control
 The cerebral circulation has dense sympathetic innervation.
 Under certain conditions, SNS stimulation can cause marked constriction of the
large and intermediate-sized cerebral arteries.
 Under many conditions in which the SNS is moderately activated.
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CBF Problems
 Stroke: a blood clot blocks the flow of blood in your cranial artery.
 Cerebral hypoxia: part of the brain doesn’t get enough oxygen.
 cerebral hemorrhage: internal bleeding in the cranial cavity.
 Cerebral edema: swelling that occurs due to an increase of water in your
cranial cavity.
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Brain Metabolism
 Resting conditions -brain metabolism:
 accounts for 15% of the total metabolism of the body.
 about 7.5 times the average metabolism of the remainder of the body.
 Most neuronal activity depends on the second-by-second delivery of glucose and oxygen from
the blood.
 Glucose delivery to the neurons its transport through cell-membrane of the neurons does not
depend on insulin.
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62. 62
Cont.
 Glucose is the obligatory energy substrate for brain and it is almost entirely oxidized to CO2 and H2O.
• Normal values for cerebral metabolic supply and demand:
• Cerebral blood flow: 50ml per 100g of tissue, per minute.
• Cerebral DO2: 150-300ml/min (Hb of 150)
• CMRO2: Cerebral Metabolic Rate of Oxygen: 3.8ml/100g/min
• Cerebral oxygen extraction ratio (CO2ER): 35-25%
• Jugular bulb venous saturation (SjvO2): 55-75%
• Cerebral glucose consumption: 6.3mg glucose per 100g per minute

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63. 63
Cont.
 CMRO2 = CBF × 1.39 × Hb × [ (SaO2 - SjvO2) + (0.03 × [PaO2 - PvO2]/100) ]
 Metabolic substrate:
 The brain normally consumes glucose and oxygen, and its RQ is 1.0
 Alternative substrates include ketones, lactate, mannose, and others
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64. 64
Cont.
 Ketone bodies are metabolites that replace glucose as the main fuel of the
brain in situations of glucose scarcity, including prolonged fasting,
extenuating exercise, or pathological conditions such as diabetes.
 Lactate is formed predominantly in astrocytes from glucose or glycogen in
response to neuronal activity signals.
 Lactate and pyruvate can sustain synaptic activity in vitro.
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65. 65
Cont.
 Mannose can sustain normal brain function in the absence of glucose.
 It crosses the BBB and in two enzymatic steps is converted to fructose-6-
phosphate, a physiological intermediate of the glycolytic pathway.
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66. 66
Cont.
 Glucose, which is taken up by facilitated diffusion via GLUTs, can
either be stored as glycogen (in the brain, the major glycogen stores
are found in the astrocytes) or metabolized in the glycolytic pathway.
 The final product of glycolysis is pyruvate, which is either transferred
into mitochondria, where it is metabolized in the citric acid cycle, or
converted to lactate.
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67. 67
Cont.
 Conversion of pyruvate to lactate is catalyzed by the oxidoreductase
lactate dehydrogenase (LDH), which reduces pyruvate to lactate and
oxidizes NADH + H+ to NAD+
 The reaction is reversible, allowing cells to either produce or consume
lactate, depending on their metabolic profile.
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68. 68
Glycolytic Pathway of Brain Metabolism
1. The Astrocyte to Neuron Lactate Shuttle.
2. Astrocytes take up glucose from the blood capillaries via glucose transporters (GLUTs).
3. In astrocytes, glucose is either stored as glycogen or metabolized to pyruvate in the
glycolysis.
4. Pyruvate is then converted to lactate by the oxidoreductase lactate dehydrogenase (LDH)
isoform 5 (LDH5).
5. The lactate is transferred from astrocytes to neurons by MCT1, MCT2, and MCT4 in
cotransport with a proton.
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69. 69
Cont.
6. MCT transport activity was found to be facilitated by interaction with the CAII and CAIV,
which catalyze the equilibrium of H+, HCO3– and CO2 both intra- and extracellularly, and
by the activity of the electrogenic sodium-bicarbonate cotransporter NBCe1.
7. In neurons, lactate is converted back to pyruvate by LDH1 and transferred into mitochondria
for aerobic energy production in the TCA.
8. In addition, glucose is directly taken up into neurons where it can either serve as energy
source in the glycolysis or is shuttled into PPP for production of NADPH and cellular
building blocks like ribose-6-phosphate.
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70. 70
Cont.
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Figure 15 - Glycolytic Pathway in Brain Metabolism

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Factors affecting cerebral metabolic rate
Table 1 - Factors which Influence the Cerebral Metabolic Rate
Increase Decrease
Vascular abnormalities Acute stages of haemorrhagic stroke Ischaemic stroke, Chronic cerebrovascular
disease
Infectious processes Fever, systemic infection Encephalitis or meningitis, Neurosyphilis
Neoplasia Glioma Paraneoplastic cerebellar degeneration
Drugs Ketamine, Amphetamine General anaesthetics
Neurological disorders Seizure Post-ictal state, Eclampsia
Physiological phenomena Stress, Anxiety, Hyperventilation Normal sleep
Trauma Traumatic brain injury
Endocrine and metabolic disorders Hepatic encephalopathy, Hypoglycaemia,
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Brain Metabolism Abnormalities
 The brain metabolic diseases are classified:
 Intoxication Disorders
 Energy Production Disorders
 Disorders of the Biosynthesis & Breakdown of Complex Molecules
 Neurotransmitter Defects
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73. 73
Cont.
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Table 2 - Classification of Brain Metabolic Diseases

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Summary
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 CBF is the blood flow to the brain.
 Supplies oxygen, glucose and nutrients.
 Removes CO2, lactic acid & metabolites.
 Cerebral vasculature has unique physiology & anatomy.
 Brain is highly vulnerable to disruption in blood flow.
 The brain normally consumes glucose and oxygen, alternative substrates include
ketones, lactate, mannose, and others

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Acknowledgement
 Firstly, I would like thanks Our Lord and Savior Jesus Christ Son of the
true Living God, Son of Theotokos.
 Next my deepest gratitude goes to my instructor Dr. Abebaye Aragaw who
gave me this chance to prepare and present on “Cerebral Blood Flow.”
 Finally, I would like to thank my classmates & the entire audience for
listening me attentively.
Habtemariam M.
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References
 Atlas of Human Anatomy (Netter Basic Science) 7th Edition
 Monro A. Observations on the structure and functions of the nervous system. Edinburgh: William Creech;
1783.
 Wright BL, Lai JT, Sinclair AJ (August 2012). "Cerebrospinal fluid and lumbar puncture: a practical
review". Journal of Neurology. 259 (8): 1530–45.
 Guyton & Hall, Medical text book of Physiology, 13th ed.
 Chapter 52 (pp. 580) Cerebral protection by Victoria Heaviside and Michelle Hayes
 McCullough, Jock N., et al. "Cerebral metabolic suppression during hypothermic circulatory arrest in
humans." The Annals of thoracic surgery 67.6 (1999): 1895-1899.
 Owen, O. E., et al. "Brain metabolism during fasting." The Journal of clinical investigation 46.10 (1967):
1589-1595.
 SCHEINBERG, PERITZ, and HAROLD W. JAYNE. "Factors Influencing Cerebral Blood Flow and
Metabolism A Review." Circulation 5.2 (1952): 225-236.
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